Goals:

After this lab you will be able to:

This lab is adapted from materials by:

Getting started

The Behavioral Risk Factor Surveillance System (BRFSS) is an annual telephone survey of 350,000 people in the United States. As its name implies, the BRFSS is designed to identify risk factors in the adult population and report emerging health trends. For example, respondents are asked about their diet and weekly physical activity, their HIV/AIDS status, possible tobacco use, and even their level of healthcare coverage. The BRFSS Web site (http://www.cdc.gov/brfss) contains a complete description of the survey, including the research questions that motivate the study and many interesting results derived from the data.

We will focus on a random sample of 20,000 people from the BRFSS survey conducted in 2000. While there are over 200 variables in this data set, we will work with a small subset.

We begin by loading the data set of 20,000 observations into the R workspace. After launching RStudio, enter the following command.

source("http://www.openintro.org/stat/data/cdc.R")

The data set cdc that shows up in your workspace is a data matrix, with each row representing a case and each column representing a variable. R calls this data format a data frame, which is a term that will be used throughout the labs.

To view the names of the variables, type the command

names(cdc)

This returns the names genhlth, exerany, hlthplan, smoke100, height, weight, wtdesire, age, and gender. Each one of these variables corresponds to a question that was asked in the survey. For example, for genhlth, respondents were asked to evaluate their general health, responding either excellent, very good, good, fair or poor. The exerany variable indicates whether the respondent exercised in the past month (1) or did not (0). Likewise, hlthplan indicates whether the respondent had some form of health coverage (1) or did not (0). The smoke100 variable indicates whether the respondent had smoked at least 100 cigarettes in her lifetime. The other variables record the respondent’s height in inches, weight in pounds as well as their desired weight, wtdesire, age in years, and gender.

  1. How many cases are there in this data set? How many variables? For each variable, identify its data type (e.g. categorical, discrete).

We can have a look at the first few entries (rows) of our data with the command

head(cdc)

and similarly we can look at the last few by typing

tail(cdc)

You could also look at all of the data frame at once by typing its name into the console, but that might be unwise here. We know cdc has 20,000 rows, so viewing the entire data set would mean flooding your screen. It’s better to take small peeks at the data with head, tail or the subsetting techniques that you’ll learn in a moment.

Summaries and tables

The BRFSS questionnaire is a massive trove of information. A good first step in any analysis is to distill all of that information into a few summary statistics and graphics. As a simple example, the function summary returns a numerical summary: minimum, first quartile, median, mean, second quartile, and maximum. For weight this is

summary(cdc$weight)

R also has built-in functions to compute summary statistics one by one. For instance, to calculate the mean, median, and variance of weight, type

mean(cdc$weight) 
var(cdc$weight)
median(cdc$weight)
  1. Compute the minimum, maximum, and average age of respondents.

While it makes sense to describe a quantitative variable like weight in terms of these statistics, what about categorical data? We would instead consider the sample frequency or relative frequency distribution. The function table does this for you by counting the number of times each kind of response was given. For example, to see the number of people who have smoked 100 cigarettes in their lifetime, type

table(cdc$smoke100)

or instead look at the relative frequency distribution by typing

table(cdc$smoke100)/nrow(cdc)

Notice how R automatically divides all entries in the table by the number of observations (using the nrow function to produce the number of rows, 20,000, in the cdc data) in the command above. This is similar to something we observed in Lab 1, when we multiplied or divided a vector with a number, R applied that action across entries in the vectors. As we see above, this also works for tables.

Also, in Lab 1, we explored the use of logical attributes (TRUE/FALSE). You can use this functionality to explore data as well. For instance, the following code produces a TRUE response for every respondent who 6 ft (72 inches) or more in height, and then summarizes the number of respondents in each category:

summary(cdc$height>=72)

  1. Summarize the number of respondents who weigh more than 175 pounds (hint: use the code above as a template).

  2. Create a numerical summary for height and age, and compute the interquartile range for each. Compute the relative frequency distribution for gender and exerany. How many males are in the sample? What proportion of the sample reports being in excellent health?

The table command can be used to tabulate any number of variables that you provide. For example, to examine which participants have smoked across each gender, we could use the following.

table(cdc$gender,cdc$smoke100)

How R thinks about data

We mentioned that R stores data in data frames, which you might think of as a type of spreadsheet. Each row is a different observation (a different respondent) and each column is a different variable (the first is genhlth, the second exerany and so on). We can see the size of the data frame next to the object name in the workspace or we can type

dim(cdc)

which will return the number of rows and columns. Now, if we want to access a subset of the full data frame, we can use row-and-column notation. For example, to see the sixth variable of the 567th respondent, use the format

cdc[567,6]

which means we want the element of our data set that is in the 567th row (meaning the 567th person or observation) and the 6th column (in this case, weight). We know that weight is the 6th variable because it is the 6th entry in the list of variable names:

names(cdc)

To see the weights for the first 10 respondents we can type

cdc[1:10,6]

In this expression, we have asked just for rows in the range 1 through 10. R uses the : to create a range of values, so 1:10 expands to 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. You can see this by entering

1:10

Finally, if we want all of the data for the first 10 respondents, type

cdc[1:10,]

By leaving out an index or a range (we didn’t type anything between the comma and the square bracket), we get all the columns. When starting out in R, this is a bit counterintuitive. As a rule, we omit the column number to see all columns in a data frame. Similarly, if we leave out an index or range for the rows, we would access all the observations, not just the 567th, or rows 1 through 10. Try the following to see the weights for all 20,000 respondents fly by on your screen

cdc[,6]

Recall that column 6 represents respondents’ weight, so the command above reported all of the weights in the data set. An alternative method to access the weight data is by referring to the name. Previously, we typed names(cdc) to see all the variables contained in the cdc data set. We can use any of the variable names to select items in our data set.

cdc$weight

The dollar-sign tells R to look in data frame cdc for the column called weight. Since that’s a single vector, we can subset it with just a single index inside square brackets. We see the weight for the 567th respondent by typing

cdc$weight[567]

Similarly, for just the first 10 respondents

cdc$weight[1:10]

The command above returns the same result as the cdc[1:10,6] command. Both row-and-column notation and dollar-sign notation are widely used, which one you choose to use depends on your personal preference.

Subsetting

It’s often useful to extract all individuals (cases) in a data set that have specific characteristics. We accomplish this through conditioning commands.

First, consider expressions like

cdc$gender == "m"

or

cdc$age > 30

These commands produce a series of TRUE and FALSE values. There is one value for each respondent, where TRUE indicates that the person was male (via the first command) or older than 30 (second command).

Special values in R

  • NA: not available, missing

  • NULL: does not exist, is undefined

  • TRUE, T: logical true. Logical is also an object class.

  • FALSE, F: logical false

Finding special values

Function Meaning
is.na Is the value NA
is.null Is the value NULL
isTRUE Is the value TRUE
!isTRUE Is the value FALSE 


absent <- NA
is.na(absent)
## [1] TRUE

Missing Data

Misssing data is particularly important

foo <- c(1, 2, NA, 3, 4)

Missing Data Challenge

  1. What is the result of 2 + NA
  2. What is the result of mean(foo)
  3. Look at the documentation of mean to change how that function handles missing values.
  4. How does median(foo) work?
  5. foo > 2. Are all the entries TRUE and FALSE?
  6. What does is.na(foo) do? What about ! is.na(foo) ?
  7. What does foo[! is.na(foo)] do?

The function na.omit is particularly useful. It removes any row in a dataset with a missing value in any column. For example,

dfrm <- data.frame(x = c(NA, 2, NA, 4), y = c(NA, NA, 7, 8))
na.omit(dfrm)
##   x y
## 4 4 8

Logical operators

< less than

<= less than or equal

> greater than

>= greater than or equal

== exactly equal to

!= not equal to

!x not equal to x

x | y x or y

x & y x and y

Subsetting with logicals

x <- c(12, 15, 8, 11, 24)
i <- c(F, F, T, F, F)
x[i]
## [1] 8
which(x < 10)
## [1] 3
x[x < 10] <- 10
x
## [1] 12 15 10 11 24

Usefel facts:

i <- c(F, F, T, F, F)
sum(i)
## [1] 1
mean(i)
## [1] 0.2
x <- c(12, 15, 8, 11, 24)
mean(x > 11)
## [1] 0.6

More on logical subsetting

Suppose we want to extract just the data for the men in the sample, or just for those over 30. We can use the R function subset to do that for us. For example, the command

mdata <- subset(cdc, cdc$gender == "m")

will create a new data set called mdata that contains only the men from the cdc data set. In addition to finding it in your workspace alongside its dimensions, you can take a peek at the first several rows as usual

head(mdata)

This new data set contains all the same variables but just under half the rows. It is also possible to tell R to keep only specific variables, which is a topic we’ll discuss in a future lab. For now, the important thing is that we can carve up the data based on values of one or more variables.

You can use several of these conditions together with & and |. The & is read “and” so that

m_and_over30 <- subset(cdc, gender == "m" & age > 30)

will give you the data for men over the age of 30. The | character is read “or” so that

m_or_over30 <- subset(cdc, gender == "m" | age > 30)

will take people who are men or over the age of 30 (why that’s an interesting group is hard to say, but right now the mechanics of this are the important thing). In principle, you may use as many “and” and “or” clauses as you like when forming a subset.

  1. Create a new object called under23_and_smoke that contains all observations of respondents under the age of 23 that have smoked 100 cigarettes in their lifetime. Write the command you used to create the new object as the answer to this exercise.

dplyr: A better way to work with data

Hadley Wickham (assistant professor of statistics at Rice, major R guru, and all-around good guy) has a knack for developing packages that make life a lot easier for R users. Two of his best packages are plyr and dplyr. Dplyr in particular is an excellent way to work with data.

Load (and if necessary install) plyr and dplyr. Note: you should always load plyr before dplyr, as the two packages have some overlapping functions that respond best when plyr is loaded first.

#install.packages(c('plyr','dplyr'))
library(dplyr)

In Hadley’s own words, the dplyr package makes data manipulation fast and easy by:

I. Elucidating the most common data manipulation operations, so that your options are helpfully constrained when thinking about how to tackle a problem.

  1. Providing simple functions that correspond to the most common data manipulation verbs, so that you can easily translate your thoughts into code.

  2. Using efficient data storage backends, so that you spend as little time waiting for the computer as possible.

dplyr provides a few core functions data manipulation. Most data manipulations can be done by combining these verbs together — something which becomes even easier with the %>% operator.

  • filter(): subset observations by logical conditions
  • slice(): subset observations by row numbers
  • arrange(): sort the data by variables
  • select(): select a subset of variables
  • rename(): rename variables
  • distinct(): keep only distict rows
  • mutate() and transmute(): adds new variables
  • group_by(): group the data according to variables
  • summarise(): summarize multiple values into a single value
  • sample_n() and sample_frac(): select a random sample of rows

At the outset, let’s focus on single-table data. These are data that are in a single dataframe or that you might find in a csv file or Excel sheet. Install and load the “Lahman” package, which contains baseball statistical data from Sean Lahman, and load the “batting” data set included in the package.

#install.packages('Lahman',repos = "http://cran.us.r-project.org")
library(Lahman)
data(Batting)
  1. Take a look at the dataset using the head and names functions, as well as other functions that you have learned so far. How many columns and rows are in the data?

At a basic level, dplyr provides you with five tools that you can use to work with a single data table. These tools are:

filter()

The filter command subsets a data table based upon each observed value. The following code filters out only Seattle Mariner’s players:

filter(Batting, teamID=='SEA')
  1. How would you save this new filtered table as a new object rather than having it simply print off in the console?

You can also filter based upon multiple attributes or for multiple values:

#only Seattle Mariners players in 2010
filter(Batting, teamID=='SEA' & yearID==2010)
#either Mariners players or San Diego Padres players
filter(Batting, teamID=='SEA'|teamID=='SDN')

The filter() function will retain all rows for which the logical query you specify is TRUE. Thus, you can also us != to filter based upon values that do not equal the specified value.

#keep all players EXCEPT Seattle Mariners players
filter(Batting, teamID!='SEA')
  1. Make a new data table that includes ONLY Atlanta Braves players (‘ATL’ is the abbreviated name in the data table) in year 2000 or later.

arrange()

The arrange command provides an easy way to sort observations. By default, the smallest value will go at the top; you can invert this using the “-”.

#sort by number of home runs, lowest to highest
arrange(Batting, HR)
#sort by number of home runs, highest to lowest
arrange(Batting, -HR)

You can also sorty by multiple attributes at the same time, including character values:

#sort by number of home runs, highest to lowest, and then by team.
arrange(Batting, -HR, teamID)
  1. Who are the top three hitters for total number of doubles (‘X2B’) hit in a single season?

mutate()

The mutate command is used to generate new variables in the data table or to edit existing variables. For instance, we can create a new category (e.g., stolen bases “SB” + home runs (“HR”) )

mutate(Batting, SBHR = SB + HR)

or modify an existing variable:

mutate(Batting, RBI = RBI + 1000)

One important thing to remember is that these changes will not be stored as part of the original object. Thus, you have to assign the mutated data table to an object name (either the same name or a new name):

Batting = mutate(Batting, SBHR = SB + HR)
  1. Generate a new variable of your choosing; be sure that the new variable is saved within the Batting data table (i.e., assign a new object)

select()

#select player id, team id, at bats, and homeruns
select(Batting, playerID,teamID,AB,HR)

sometimes, you want to drop one or two columns and keep the rest. It can be incredibly cumbersome to insert all the names that you want to keep. Instead, you can invert the select() function, again using the “-” sign, to drop a specified variable:

#drop homeruns from datatable
select(Batting, -HR)
  1. Generate a data table that includes every variable except “G” and “G_batting”.

summarise()

Finally, the summarise command can be used to generate summary statistics. For instance, you can compute the mean or median of a given variable. Note that the summarise command is slightly different than some other operations, in that the variable you want to summarise must be called within the function you want.

summarise(Batting,mean(HR,na.rm=T))

Note also that you need to select na.rm=T within the mean function, otherwise the function will choke on the presence of NA values. Setting na.rm=T tells R to ignore NA values when computing the variable mean. You can request multiple summaries:

summarise(Batting,mean(HR,na.rm=T),mean(SB,na.rm=T))
summarise(Batting,mean(HR,na.rm=T),sd(HR,na.rm=T))

or, you can use the summarise_each() function to do the same thing. Notice that the “.” stands in for each variable, and then you select na.rm=T within each function.

summarise_each(Batting,funs(min(.,na.rm=T),max(.,na.rm=T)),HR,SB)

group_by()

You might be wondering what the point is of the summarise and summarise_each functions since as-of-yet we have used them to do operations that we can already do quite easily with base functions such as min(), max(), and mean() (e.g., mean(Batting$HR,na.rm=T)).

The group_by function is a key addition that greatly multiplies the power of dplyr, as it allows us to compute grouped summary values, for instance the maximum number of homeruns hit in a season for each team:

summarise(group_by(Batting,teamID),mean(HR,na.rm=T))
## Source: local data frame [149 x 2]
## 
##    teamID mean(HR, na.rm = T)
## 1     ALT           0.1176471
## 2     ANA           4.6784452
## 3     ARI           3.7345254
## 4     ATL           3.7478216
## 5     BAL           4.7729167
## 6     BFN           0.8606557
## 7     BFP           0.7692308
## 8     BL1           0.5000000
## 9     BL2           0.6903553
## 10    BL3           0.8888889
## ..    ...                 ...
  1. Using the summarise and group_by functions, generate a summary table showing the maximum number of stolen bases (SB) and triples (X3B) for each team by a batter in a single season.

chaining functions

Finally, perhaps the coolest feature of dplyr is that you can daisy chain functions together. dplyr imports a special function `%>%’ from the magrittr package to do this. Typically, when working with data you will perform a series of operations; dplyr allows you to link these operations together without needing to generate a series of intermediate objects.

Basically, you do this by starting with the data table (Batting in this case) and then using the “%>%” operator to link functions. Within a chain, you do not need to place the data table name within each operation function:

Batting %>% filter(AB>400,yearID>1990) %>% group_by(teamID) %>% summarise(max(SB))

  1. Using the chaining technique, identify the minimum number of hits (H) made in a single season by a player on each team who had at least 400 at-bats (AB) in a single season since year 2000.

  2. Using a combination of filter, select and and slice show only year and homeruns of Seattle Mariners players for the first two observations (i.e., just the first two rows)

ggplot

Plotting with ggplot2

We will be using the graphics package ggplot2, which is one of the most popular, but it is only one of several graphics packages in R.[^1]

Unlike many other graphics systems, functions in ggplot2 do not correspond to separate types of graphs. There are not scatterplot, histogram, or line chart functions per se. Instead plots are built up from component functions.

  1. Data
  2. Aesthetics: Maps variables in the data to visual properties: position, color, size, shape, line type …
  3. Geometric objects: The specific shapes that are drawn: points, lines,
  4. scales: How variables values map to “computer” values.
  5. stat: summarize or transform the data. e.g. bin data and count in histogram; run a regression to get a line.
  6. facet: create mini-plots of data subsets

Install and load the gapminder package, which provides an excerpt of data from Gapminder.org concerning worldwide development statistics. Don’t forget to load ggplot2 as well!

Initializing a plot object

ggplot(gapminder, aes(x = gdpPercap, y = lifeExp))

This gives an error message because there is nothing to plot yet!

Storing plot object

This just initializes the plot object, it is better if you assign it to an object, p is good enough

p <- ggplot(gapminder, aes(x = gdpPercap, y = lifeExp))

Now we can add geoms

p + geom_point()

That look okay but it would probably look be better if we log transform

p_l <- ggplot(gapminder, aes(x = log10(gdpPercap), y = lifeExp))
p_l + geom_point()

A better way to log transform

p + geom_point() + scale_x_log10()

Let’s make that stick

p <- p + scale_x_log10()

Common workflow: gradually build up the plot you want, re-define the object ‘p’ as you develop “keeper” commands. Note that in the reassigning we excluded the geom. Now, set the contenent variable to the aesthetic category color:

p + geom_point(aes(color = continent))

In full detail, up to now:

ggplot(gapminder, aes(x = gdpPercap, y = lifeExp, color = continent)) +
  geom_point() +
  scale_x_log10()

Let’s address over-plotting: SET alpha transparency and size to a value

p + geom_point(alpha = (1 / 3), size = 3)

Add now a fitted curve or line

p + geom_point() + geom_smooth()
## geom_smooth: method="auto" and size of largest group is >=1000, so using gam with formula: y ~ s(x, bs = "cs"). Use 'method = x' to change the smoothing method.

p + geom_point() + geom_smooth(lwd = 2, se = FALSE)
## geom_smooth: method="auto" and size of largest group is >=1000, so using gam with formula: y ~ s(x, bs = "cs"). Use 'method = x' to change the smoothing method.

p + geom_smooth(lwd = 1, se = FALSE, method = "lm") + geom_point()

That’s great but I actually want to revive our interest in continents!

p + aes(color = continent) + geom_point() + geom_smooth(lwd = 3, se = FALSE)
## geom_smooth: method="auto" and size of largest group is <1000, so using loess. Use 'method = x' to change the smoothing method.

Facetting: another way to exploit a factor

p + geom_point(alpha = (1 / 3), size = 3) + facet_wrap(~ continent)

Still want lines? Let’s add them

p + geom_point(alpha = (1 / 3), size = 3) + facet_wrap(~ continent) +
  geom_smooth(lwd = 2, se = FALSE)
## geom_smooth: method="auto" and size of largest group is <1000, so using loess. Use 'method = x' to change the smoothing method.
## geom_smooth: method="auto" and size of largest group is <1000, so using loess. Use 'method = x' to change the smoothing method.
## geom_smooth: method="auto" and size of largest group is <1000, so using loess. Use 'method = x' to change the smoothing method.
## geom_smooth: method="auto" and size of largest group is <1000, so using loess. Use 'method = x' to change the smoothing method.
## geom_smooth: method="auto" and size of largest group is <1000, so using loess. Use 'method = x' to change the smoothing method.

Challenge

  • plot lifeExp against year
  • make mini-plots, split out by continent
  • add a fitted smooth and/or linear regression, w/ or w/o faceting
# plot lifeExp against year
# y <- ggplot(gapminder, aes(x = year, y = lifeExp)) + geom_point()
#print(y)

# make mini-plots, split out by continent
# y + facet_wrap(~ continent)

# add a fitted smooth and/or linear regression, w/ or w/o facetting
#y + geom_smooth(se = FALSE, lwd = 2) +
#  geom_smooth(se = FALSE, method ="lm", color = "orange", lwd = 2)

# y + geom_smooth(se = FALSE, lwd = 2) +
#  facet_wrap(~ continent)

What if I am only interrested in the US?

ggplot(filter(gapminder, country == "United States"),
       aes(x = year, y = lifeExp)) +
  geom_line() +
  geom_point()

Let just look at five countries

some_countries <- c("United States", "Canada", "Rwanda", "Cambodia", "Mexico")
ggplot(filter(gapminder, country %in% some_countries),
       aes(x = year, y = lifeExp, color = country)) +
  geom_line() +
  geom_point()

So what’s up with Mexico?

  • Nafta? Higher GDP?

Not really…

ggplot(subset(gapminder, country %in% some_countries),
       aes(x = year, y = lifeExp, color = country)) +
  geom_line() +
  geom_point(aes(size=gdpPercap))

You can change the way the plot looks overall using theme

ggplot(subset(gapminder, country %in% some_countries),
       aes(x = year, y = lifeExp, color = country)) +
  geom_line() +
  geom_point(aes(size=gdpPercap)) +
  theme_minimal()

In addition to the themes included with ggplot, several other themes are available in the ggthemes package.

Version Control

start a project and keep it under version control

Live demo

Questions?

submit your homework via git

Questions?

Goal check

motivation for next class